If a prince is born second and direct in the line of succession, and his father dies, does he become the new crown prince? I believe that the title Hereditary Prince is used in some kingdoms, to denote a direct heir is not first in line to the throne ...
Of course, it is also used to denote the heir-apparent to a principality (e.g. Monaco and Liechtenstein). It goes without saying that the title Crown Prince is never used in those places -- or even in grand duchies (e.g. Luxembourg).
Can "Crown Prince" actually be used for an heir-presumptive who is first in line to the throne -- with the understanding that the said person can lose that designation?